There is some intriguing things about DES and 3DES. Now, I know that DES is weak and 3DES was an attempt to construct a more secure block-cipher from a deprecated one.
Having this in mind, what about the composition of two independent instantiations of block-cipher (t.i.t.s with two independent keys) having a reduced number of rounds. Take the example of AES (with key of 128-bit) which has 10 rounds (and consider that the last round is complete, in the sense that it contains all the operations add-roundkey, mixcolumns, shiftrows and subbytes). If we consider a reduced version of AES with 5 complete rounds, denoted $AES^r$, and we construct a new block cipher in the following way:
$$AES'_{k_1,k_2}(.)=AES^r_{k_1}(AES^r_{k_2}(.))$$
Is this block cipher as secure as the original version of AES ? It seems to me that it does, since the keys are independant, but I need confirmation.
Edit: Is the following composition also secure ?
$$AE''_{k_1,k_2}(.)=AES^r_{k_1}({AES^{r}}^{-1}_{k_2}(.))$$
where ${AES^r}^{-1}_{k_2}(.)$ denotes the decryption operation.
Thank you.